Noises may be characterized as sounds that are not pleasant to human ears. Among the noises, white noise is often used as a simulation source in the engineering field due to its uniformly distributed power density in the frequency domain. Pink noise, on the other hand, is often used as a source for frequency response measurements on stereo systems. Instead of being flat in the linear frequency domain, pink noise, as opposed to white noise, has energy uniformly distributed over octaves. More specifically, the total energy of each pink noise octave has substantially the same value over a given frequency range, for example, 20 Hz to 20 kHz. This resembles the psycho-acoustic model of human hearing, specifically, as the frequency increases, the ear is less sensitive to the frequency change by, for example, a factor of 2.
There are generally two methods for generating pink noise in real time that are conventionally focused on time domain processing; 1) filtering white noise and 2) the Voss algorithm. The filtering white noise method generates a white noise signal using random number generators and then passes the white noise through a low pass filter. The disadvantage of this method is that a low pass filter with a proper frequency response is very difficult to construct. Therefore, the quality of the pink noise generated by this method may largely depend on how well the filter is designed. Because it is difficult to construct a suitable digital filter operating in the time domain, a pink noise generated by this method is problematic.
Another method uses the Voss algorithm. This is a very well known method that also starts with white noise generated by some random number generator. White noise generated for different octaves are then added together to yield a signal very close to a pink noise signal. Using this method, however, a 1 db deviation from the perfect pink noise spectrum may be created that cannot be eliminated no matter how many octaves or samples are used.
Besides the aforementioned problems, there is another disadvantage in using the methods described above. For both methods, because the signal is generated by random process, a very large sample space is needed to show the expected statistical behavior. Specifically, in order to get a good measurement, the source must generate for a long time in order to produce a satisfactory pink noise